Journal of Physical Education and Sport ®(JPES),Vol 21 (Supplement issue 2), Art 121 pp 974– 983, Apr.2021 online ISSN: 2247 - 806X; p-ISSN: 2247 – 8051; ISSN - L = 2247 - 8051 © JPES

Original Article

Influence of the 2020 pandemic on speedway – managerial implication

SYLWESTER BEJGER The Faculty of Economic Sciences and Management, Nicolaus Copernicus University, Toruń,

Published online: April 30, 2021 (Accepted for publication April 15, 2021) DOI:10.7752/jpes.2021.s2121

Abstract : The season of the year 2020 was characterized by a number of difficulties and extraordinary organizational and management conditions for many sports disciplines. One of the disciplines most affected by the restrictions caused by the pandemic was motorcycle speedway. Suffice it to say that out of all European leagues, only the Polish league and the Swedish league completed the 2020 season. Moreover in both countries the games started with a long delay and were not preceded by typical preparatory activities for the season, such as sparring matches or individual tournaments. Focusing on Polish highest level league, the PGE , the paper contains careful statistical and exploratory analysis of data sample encompassing seasons 2015 to 2020, aiming on discovery if and how season 2020 differed from previous ones. This analysis was carried out in the scope of three data sets with different levels of aggregation, concerning meetings, teams and heats of individual riders. The analysis covered the general performance of a whole sample o riders, performance and demographic structure of teams, and results of heat per rider, taking account rider’s nationality and age. The results of the analysis made it possible to identify changes in selected metrics describing the effectiveness of teams and players, probably caused by structural difference of 2020 season. This allows for the formulation of conclusions supporting the management of the teams and clubs in decision making process concerning team’s profile and riders and track preparation. Such conclusions can help coaches mitigate the impact of unfavorable external conditions on team quality and individual player preparation in similar circumstances in a future. Key Words : - team management, motorcycle speedway, data mining, demographic and internationalization, impact of pandemic on sport

Introduction Motorcycle speedway (or speedway in short, when misunderstanding is impossible) was created in Australia at the beginning of the 1920s (May, 1978). Speedway in Poland started in 1930 (Błaszkowska, 2018). Currently, speedway in Poland plays an especially important role in the economic, social and sports sense. Contrary to other countries, this sport is very popular in Poland and ranks 9th on the by popularity (Report, 2021). The meeting of the Polish highest level league, PGE Ekstraliga alone gathered around 700,000 fans in the 2019 season (PGE statistics, 2021). PGE Ekstraliga is considered as one of the most important speedway leagues in a world. Speedway is an individual sport in which trained skill plays a central role, allowing us to understand speedway not as mere sport, but as art (Siitonen et al. 2020). However, the success of the team is the sum of not only the individual efforts of the players, but also depends on the proper strategy of team building and preparation, as well as preparation of a home track. As all of the motorsports, it is an expensive discipline either. There is no doubt that the pandemic season of 2020 has seriously disrupted the functioning of speedway leagues and the training and competition cycle of the riders all over the world. Due to worldwide lockdown only PGE Ekstraliga and Swedish Eliteserien started and finished 2020 season in Europe (season started with significant delay in that countries, 12.06 and 01.08 respectively). In Poland, due to restriction imposed by authorities there were no usual spring, preliminary speedway events (individual tournaments, sparring meetings) and the number of trainings in a track for riders was significantly limited, either. Moreover, even after starting of the league the meetings were held partly without fans and partly with 50% participation of them. Taking into consideration the obvious abnormalities of season 2020 and above mentioned, special importance of a speedway and speedway league for Polish sport and socio-economical life in general, the question of impact of the season’s 2020 conditions on performance of the teams and riders seems to be very important. The main research goal of the paper is to find some distinctive changes of 2020 season’s parameters by mining a statistical data. Such findings could lead to conclusions that could be useful for the management of the teams and decisions making process of building team’s profile, taking into account both demographic aspect and internationalization. As in the other disciplines of sport (see for example Gulak – Lipka, 2020) role of globalization and internationalization in speedway is increasing. Improper management may lead to financial 974------Corresponding Author: SYLWESTER BEJGER, E-mail: [email protected] SYLWESTER BEJGER ------difficulties, which in turn might result in bankruptcy of the club (Lis, Tomanek, 2020), especially in a macroeconomic crisis environment.

Material & methods The following research methods have been used to achieve the assumed research goal: statistical data mining, descriptive, comparative and subject literature analysis. The main body of the research is statistical examination and inference leading to comparative analysis. Time period of the research covers seasons 2015 – 2020 of speedway PGE Ekstraliga in Poland. Author used data 1 collected by the portal http://gurustats.pl . Dataset is divided in three logical parts, namely data on meetings, data on teams and data on riders per meeting. For the purposes of the study, author chose an appropriate subset of the features. Detailed description of variable used in particular part of the research is provided in a Results section.

For the research the following exploratory methods have been used. Statistical visualization (histograms, scatter plots and a kernel density estimate (KDE) plot). A histogram aims to approximate the underlying probability density function that generated the data by binning and counting observations. Kernel density estimation (KDE) plot smooths the observations with a Gaussian kernel, producing a continuous density estimate (Hastie, et al. 2009). Selected statistical tests used: D’Agostino and Pearson’s (1973) omnibus test of normality, Epps-Singleton (1986) ES test whether two samples are generated by the same underlying distribution, equality of variance Levene (1960) test. Levene’s test is an alternative to Bartlett’s test in the case where there are significant deviations from normality. In a part of the research connected with cluster analysis the Kruskal-Wallis H-test (2001) was adapted. This test is a non-parametric version of ANOVA and tests the null hypothesis that the population median of all of the groups sampled from are equal. For correlation assessment the Spearman (1903) rank-order correlation coefficient was used. This test is a nonparametric measure of the monotonicity of the relationship between two datasets. Unlike the Pearson correlation, the Spearman correlation does not assume that both datasets are normally distributed. To calculate Spearman rs for a sample of size n, values of variables Xi and Yi are converted to its ranks rg X and rg Y and use to compute:

(1) where: cov( rg X, rg Y) is the covariance of the rank variables, rgX , rgY are the standard deviations of the rank variables.

Important part of the research is the cluster analysis. For that task K-Means algorithm (1957, 1965) was used. The K-Means algorithm divides a set of ͈ samples ͒ into k disjoint clusters ̽, each described by the mean ͞ of the samples in the cluster. The means are called the cluster “centroids”. The K-Means algorithm aims to choose centroids that minimize the criterion so called inertia, which is within-cluster sum of squares:

(2) Inertia can be recognized as a measure of how internally coherent clusters are. The number of clusters k can be determined according to inertia or mean silhouette coefficient over all the instances. An instance's silhouette coefficient is equal to ( ͖−͕)/max( ͕,͖) where ͕ is the mean distance to the other instances in the same cluster (it is the mean intra-cluster distance), and ͖ is the mean nearest-cluster distance, that is the mean distance to the instances of the next closest cluster (defined as the one that minimizes ͖, excluding the instance's own cluster). The silhouette coefficient can vary between -1 and +1: a coefficient close to +1 means that the instance is well inside its own cluster and far from other clusters, while a coefficient close to 0 means that it is close to a cluster boundary, and finally a coefficient close to -1 means that the instance may have been assigned to the wrong cluster.

Results The first part of the empirical research starts with analysis of the meetings in a sample period. The main research question was whether the 2020 season was statistically significantly different from other seasons in terms of overall results and general performance of the riders. As a proxy measure of performance the Best Heat Time of a meeting was used. Three variables connected with results were also included in the study. Descriptive statistics of examined features are depicted in Table 1 2.

1 Data available commercially on request. 2 All of the Tables and Figures in a paper present author’s own results. ------975 JPES ® www.efsupit.ro SYLWESTER BEJGER ------Table 1. Descriptive statistics - meetings stat\season 2015 2016 2017 BHT* Pts_H Pts_A Pts_diff BHT Pts_H Pts_A Pts_diff BHT Pts_H Pts_A Pts_diff count 64 64 64 64 64 64 64 64 64 64 64 64 mean 62.77 49.17 40.63 11.55 62.98 49.19 40.53 12.75 62.04 47.72 41.20 10.08 std 3.60 6.01 6.00 9.09 4.06 6.74 6.31 8.89 3.16 6.16 6.15 7.78 min 57.41 36 27 0 56.40 29 28 0 56.50 31 17 0.00 25% 60.24 45 37 5.5 59.56 45 35.75 6 59.52 44 38 3.75 median 61.09 49 40.5 10 61.46 49.5 40.5 11 61.06 48 41 9.00 75% 65.24 53 45 16 66.18 54 45 20 64.81 52 45.25 14.00 stat\season 2018 2019 2020 count 64 64 64 64 64 64 64 64 63 63 63 63 mean 62.73 48.80 41.09 11.20 62.55 48.16 41.78 11.31 62.51 47.83 41.22 13.56 std 3.67 5.47 5.54 7.30 2.70 6.19 6.20 8.04 2.85 8.17 8.05 9.67 min 58.42 28 29 0 58.29 31 26 0 57.43 29 25 0 25% 59.44 46 37 6 60.57 44 38 6 60.07 42.5 35.5 4.5 median 61.82 49 40.5 11 61.49 49 41 10 62.16 48 40 14 75% 65.47 52.25 44 16 64.70 52 46 14 65.15 53 47 20 *BHT - Best Heat Time of a meeting (seconds); Pts_H - number of points collected by home team; Pts_A - number of points collectd by away team; Pts_diff - absolute value of a difference ( Pts_H - Pts_A ) Analyzing Table 1 one can observe similarities in a mean and median of BHT across all seasons and some differences in Pts_diff descriptive statistics in season 2020. In a next step visual explorations of the features was conducted. Fig.1 Histograms and KDE - BHT

Fig.2 Histograms and KDE – Pts_diff

Fig.3 Scatter plots and regression lines – Pts_diff vs Meeting_no

Fig.4 Scatter plots and regression lines – Pts_H vs Meeting_no

Fig.5 Scatter plots and regression lines – Pts_A vs Meeting_no

976 ------JPES ® www.efsupit.ro SYLWESTER BEJGER ------The visual explorations shows that the empirical distributions of both the studied variables differed over the seasons (Fig. 1 and 2). From Fig. 3 to 5 one can learn that variance of difference in meeting’s score was exceptionally high in a season 2020, mostly due to higher variance of home points. That suggest a more balanced ratio of home and away wins. Content of Table 2 confirms that observation. Table 2. Meeting results - counts ratio season Win_H* Win_A Draw Win_A/Win_H 2015 47 13 4 0.255 2016 47 14 3 0.280 2017 38 19 7 0.422 2018 49 10 5 0.185 2019 44 17 3 0.362 2020 41 19 3 0.432 *Win_H – number of home wins, Win_H – number of away wins To explore if season 2020 was structurally different in terms of the mean, variance and empirical distributions statistical test were performed next. Usual normality test was performed at first to check if standard normality assumption could be use in further examination. The results of this test and the values of third and fourth central moments reports Table 3. Table 3. Normality test, skewness and kurtosis BHT Pts_diff BHT Pts_diff season test_stat p-value test_stat p-value skewness kurtosis skewness kurtosis 2015 12.24 0.002 10.74 0.005 0.598 -1.019 1.003 0.368 2016 62.19 0.000 6.41 0.041 0.227 -1.475 0.498 -0.821 2017 9.41 0.009 10.92 0.004 0.579 -0.927 0.867 1.063 2018 12.34 0.002 7.39 0.025 0.544 -1.040 0.697 0.726 2019 9.94 0.007 10.03 0.007 0.423 -1.008 0.892 0.688 2020 23.41 0.000 3.79 0.150 0.209 -1.274 0.571 -0.332 The null hypothesis of that test is: feature comes from a normal distribution. Assuming standard significance level of 5% only in one case we cannot reject hypothesis of normality (yellow marked). Similarity of empirical distributions was checked next. The null hypothesis that two seasons have the same underlying probability distribution of examined features was tested by the ES test. The equality of variance and mean was tested in following stage of research. The strategy of testing was testing all season in pairs. Testing season 2020 against cumulative sample of seasons 2015 to 2019 was considered as less restrictive, so driving to less clear conclusions. The results of that test contain Table 4. It reports p-values of tests of season 2020 against all other season in a sample period. Table 4. Comparative statistical tests - meetings EPS test test of variance test of mean BHT Pts_diff BHT Pts_diff BHT Pts_diff season p-value p-value p-value p-value p-value p-value 2015 0.001 0.413 0.317 0.320 0.654 0.230 2016 0.000 0.651 0.001 0.881 0.450 0.626 2017 0.148 0.131 0.868 0.037 0.374 0.027 2018 0.028 0.178 0.036 0.005 0.707 0.124 2019 0.662 0.426 0.515 0.045 0.940 0.157 Yellow marked p-values signal rejection of a null hypothesis on 5% significance level. Second part of the research was the examination of data connected with teams. Considering the aim of the examination two important measures were selected for analysis: number of points collected by team in a meeting ( Pts ) and average age of a team in a meeting ( AAT ), calculated as average age of the riders participating in each meeting. Pts is considered as a proxy measure of average team performance in meeting and season, AAT is demographic information connected with team management and policy. Main goal of that part was to discover any patterns and changes in that patterns in a relation of age of a team and team performance. Descriptive statistics of examined features are depicted in Table 5. Table 5. Descriptive statistics - teams stat\season 2015 2016 2017 Pts AAT Pts AAT Pts AAT count 8 8 8 8 8 8 mean 44.70 26.74 44.56 27.21 44.15 27.14 std 2.86 1.92 3.34 1.92 2.84 2.43 min 38.36 23.93 39.00 24.56 40.71 24.08 25% 44.44 25.43 42.68 25.99 41.88 25.52 median 45.04 26.80 44.07 27.43 43.44 26.85 75% 46.17 28.21 47.38 28.19 47.01 28.27 stat\season 2018 2019 2020 count 8 8 8 8 8 8 ------977 JPES ® www.efsupit.ro SYLWESTER BEJGER ------mean 44.68 26.22 44.69 26.81 44.31 27.01 std 2.90 1.58 3.59 1.83 4.92 2.00 min 41.50 22.93 39.50 23.99 34.93 24.61 25% 42.36 25.83 42.91 25.80 43.18 25.33 median 44.34 26.29 44.51 27.12 44.84 26.99 75% 46.29 27.13 45.49 27.70 47.15 28.86

In a next step visual explorations of the features was conducted. Fig. 6 Histograms and KDE – Pts

Fig. 7 Histograms and KDE – AAT

Figures 6 and 7 show interesting oddity of both varables’ empirical distributions in season 2020. In case of Pts empirical distribution has heavier tails and is more platykurtic than in the other seasons, in a case of AAT there is distinctive bimodal distribution.

Table 6. Normality test, skewness and kurtosis - teams Pts AAT Pts season test_stat p-value test_stat p-value skewness kurtosis 2015 0.10 0.951 83.47 0.000 0.000 0.011 2016 3.87 0.144 5.97 0.051 -0.037 -0.647 2017 8.93 0.012 8.79 0.012 -0.406 1.210 2018 2.28 0.320 7.46 0.024 -0.007 -0.551 2019 0.19 0.912 1.22 0.543 0.006 -0.259 2020 3.66 0.160 5444.97 0.000 -0.028 -0.641 As expected from visual inspection, there is no reason to reject a hypothesis of normality of distribution of Pts population (expect 2017 season), and one could reject a hypothesis of normality of AAT distributions in almost every case. Furthermore, the value of kurtosis in 2020 confirms observation of platykurtic shape of distribution of Pts in 2020 season.

Table 7. Comparative statistical tests - teams EPS test test of variance test of mean Pts AAT Pts AAT Pts AAT season p-value p-value p-value p-value p-value p-value 2015 0.162 0.082 0.021 0.081 0.712 0.151 2016 0.625 0.000 0.189 0.002 0.747 0. 216 2017 0.007 0.000 0.002 0.737 0.949 0.725 2018 0.021 0.000 0.005 0.000 0.666 0.001 2019 0.067 0.000 0.009 0.023 0.653 0.664 The main object of that part of research is detection of demographic pattern in teams’ performance. Moving to this step author stared from visual inspection of relation between variables Pts and AAT . Fig 8 depicts bivariate KDE plot of Pts and AAT features by seasons.

Fig. 8 Bivariate KDE – PTS and AAT

Figure 9 contains scatter plots (plus regression lines) of Pts vs. AAT in all of the seasons in a sample.

978 ------JPES ® www.efsupit.ro SYLWESTER BEJGER ------Fig. 9 Scatter plots and regression lines - Pts vs. AAT

In Fig. 8 one can notice very interesting and distinctive pattern of KDE in 2020 season. There are two clear clusters of average age and team/points distribution. We cannot observe similar, in terms of size and shape, clusters in the previous seasons. Fig. 9 confirms such pattern via explicit grouping of points collected by teams around two values of average age. Moreover, one can preliminary asses direction of correlation between two variables of interest. In all seasons, expect season 2016, one can observe weak, negative correlation between number of points and average age. In a season 2020 there is no correlation at all. Above mentioned observations need be confirmed by deeper investigation. To conduct the research, in a next steps the author utilized statistical test of correlation coefficient and unsupervised learning method of clustering. Table 8 contains values of Spearman rank-order correlation coefficient rho and p-values for null hypothesis of value of zero of that coefficient.

Table 8. Spearman correlation coefficient - Pts vs. AAT season Spearman rho p-value 2015 -0.23 0.009 2016 0.12 0.168 2017 -0.23 0.010 2018 -0.25 0.004 2019 -0.16 0.077 2020 0.02 0. 848 Results reported in Table 8 confirms visual assessment. There is a weak, negative, statistically significant correlation between points collected by team and team’s average age in all of the seasons, expect seasons 2020 and 2016. In a season 2020 the lack of correlation is evident in terms of both rho and p-value, when the result for 2016 is more vague. In a next step the author performed cluster analysis to determine if the age clusters in fact exists, what is the number of clusters and if the median of points collected by the teams in clusters is significantly different. The well-known K-Means algorithm was used. Taking into account the results of visual analysis and analysis of correlation, the cluster study was carried out against two samples - sample of season 2020 and sample encompassing seasons 2015 to 2019. First task was to determine k (number of clusters) in samples. For that two methods were applied: inertia plot and silhouette coefficient plot. Inertia measure the distance between each instance and its centroid. Plotting the inertia as a function of ͟ allow visually determine optimal number of clusters. Mean silhouette coefficient plot shows value of coefficient for various k. One look for argmax(silhoutte).

Fig. 10 Inertia and silhoutte scores – season 2020 (left panel) and seasons 2015-2019 (right panel).

Clearly, in a season 2020 existed two clusters according to the average age of the teams (both inertia and silhoutte point to k = 2). In the rest of a sample one can observe 5 to 8 clusters (silhoutte), with 5 supported by inertia. The next phase of cluster analysis was determination of centroids and testing if the medians of number of points collected by teams in clusters were significantly different. For medians equality test the Kruskal-Wallis H-test was performed. The null hypothesis of that test states that the population median of all of the clusters in a sample are equal.

------979 JPES ® www.efsupit.ro SYLWESTER BEJGER ------Table 9. Analysis of clusters in the samples Seasons Season 2020 2015 - 2019 Median number of points Centroid cluster 1 Centroid cluster 1 28.83 25.64 cluster 3 45.00 Mean number of points Mean number of points cluster 1 Centroid cluster 4 cluster 1 44.32 45.77 27.33 Median number of points Median number of points Mean number of points cluster 4 cluster 1 44.00 cluster 1 45.50 44.74 Median number of points Centroid cluster 2 Centroid cluster 2 25.11 28.98 cluster 4 44.00 Mean number of points Mean number of points cluster 2 Centroid cluster 5 cluster 2 44.71 43.05 31.16 Median number of points Median number of points Mean number of points cluster 5 cluster 2 45.50 cluster 2 43.50 42.29 Median number of points Centroid cluster 3 23.79 cluster 5 41.00 Mean number of points cluster 3 45.86 The Kruskal-Wallis H - 15.87 0.099 The Kruskal-Wallis H - statistics statistics 0 p-value 0.753 p-value 0.003 Findings presented in Table 9 confirm preliminary observations made on the basis of visualization.

In the final part of a research author focus on individual meeting/rider data. As the results of that part are extensive, this paper contain only the most important ones from the point of view of the aim of examination. The analysis was done in two main directions – influence of a an age of a rider and nationality of a rider on performance in seasons. Each individual meeting/rider data record was tagged as belonging to rider of age (taken at the date of the heat) under or equal 25 years (“Younger” group) and above 25 years (“Older” group) and as “Polish” or “other” (polish nationality or other nationality of a rider). The split age was chosen on a basis of cluster analysis. At first the influence of age of a rider on performance by seasons was examined. Table 10 contain the most important findings.

Table 10. Impact of an age of a rider on exeptions and points collected Binomial Exceptions Points collected Correlation coefficient test rider Spearman season defects exclusions falls count sum mean median group season rho p-value p-value 2015 Older 33 44 7 460 3534 7.68 8 2015 0.33 0.000 0.464 Younger 28 50 7 429 2213 5.16 4 2016 0.45 0.000 0.989 2016 Older 34 32 7 459 3790 8.26 9 2017 0.37 0.000 0.126 Younger 36 35 2 431 1952 4.53 3 2018 0.53 0.000 0.630 2017 Older 29 41 6 483 3731 7.72 8 2019 0.46 0.000 0.201 Younger 23 36 8 412 1960 4.76 4 2020 0.48 0.000 0.000 2018 Older 21 39 6 503 4021 7.99 9 Younger 25 25 5 492 1732 3.52 2 2019 Older 18 32 4 504 3857 7.65 8 Younger 18 22 6 489 1899 3.88 3 2020 Older 18 27 4 516 3959 7.67 8 Younger 12 27 11 457 1651 3.61 3 Analyzing exceptions the author assumed that only number of falls could be connected with potential abnormalities of season 2020 (as defects and exclusion are rather caused by endogenous or technical reasons). In fact in a 2020 season one can observed the highest number of falls of “Younger” riders in a whole sample. Column “Binomial test” of Table 10 contain p-values for null hypothesis of equality of probabilities of fall in a group of “Younger” and “Older”, when probability of fall is modelled by binomial distribution. As one can see, only in season 2020 probability of fall of a young rider was significantly greater than probability of fall of older rider. Moving to analysis of performance of groups of younger and older riders, measured by the number of points collected by season, one can notice that in season 2020 older riders started 516 times (the highest number in a whole sample) and collected second highest sum of points in all of the seasons. Younger riders perform much worse, with the smallest sum of points collected and second smallest mean of points. It suggest that positive correlation between age and number of points collected by the rider should exists. The column “Correlation coefficient” of Table 10 contains both values of Spearman Correlation coefficient and p-values of test for no correlation. In all of the seasons there were statistically significant, positive correlation between variables in consideration. This result may seem to contradict the findings of the second part of the study, which showed a negative correlation or no correlation between the mean age and the number of points (see. Table 8). However, the contents of Table 8 refer to the average age of the teams, while those of Table 10 refer to the

980 ------JPES ® www.efsupit.ro SYLWESTER BEJGER ------relationship between the average age of the rider and the points scored. So in author’s opinion these results supports each other, especially for 2020 season. In Table 11 some preliminary results on relation of nationality and sport performance of a rider are shown. Table 11. Impact of nationality on performance season nationality count sum mean std coefficient of variation 2015 other 324 2694 8.31 4.02 48.3% Polish 565 3053 5.40 4.22 78.1% 2016 other 328 2698 8.23 3.89 47.3% Polish 562 3044 5.42 4.06 75.0% 2017 other 313 2455 7.84 3.83 48.8% Polish 582 3236 5.56 4.02 72.3% 2018 other 372 2637 7.09 4.63 65.3% Polish 623 3116 5.00 4.28 85.5% 2019 other 411 2974 7.24 4.31 59.6% Polish 582 2782 4.78 4.19 87.7% 2020 other 397 3044 7.67 4.22 55.0% Polish 576 2566 4.45 4.10 92.1% If better average score of international riders are obvious to some extent (one of the reason is that junior riders in PGE Ekstraliga must be Polish), then two numbers of season 2020 (yellow marked) are something extraordinary. In that season international riders collected maximal sum of points in a whole sample and Polish riders demonstrated highest level of variation of points collected in the meetings (international riders showed level of that measure fairly similar to previous ones).

Discussion The present study is, to the best of the author's knowledge, the first of its kind to be undertaken after the first pandemic season in speedway. Focusing on one of the most important speedway leagues in the world, the Polish PGE Ekstraliga, the study led to the formulation of several important observations regarding the impact of the turbulence of the 2020 season on the results of teams and players. The analysis showed that season 2020 was similar to the rest of the sample in terms of average results of the teams. However, deeper investigation revealed some distinctive and important patterns. Examination confirmed that average performance of the best group of riders in league, measured by BHT, was not significantly different in season 2020 and previous 5 seasons in terms of mean time of a heat. It means that winner’s group of riders was performing similar to non-covid seasons. However empirical distribution of BHT in 2020 was significantly different in 3 cases of 5, which suggests that there was structural changes in performance distribution. In fact, analyzing skewness and kurtosis of empirical distributions one can say that BHT in was distributed more flat than in previous years (apart 2016 season), which can means that preparation of tracks in 2020 season was more diverse (supports both faster and slower wins) than in previous seasons. Moving to difference in scores (Pts_diff), this metric describes an average sport level of teams in a season. One can observe that internal distributions of that measure are not statistically different across all seasons, however there are significant difference in variability of it (in 3 from 5 seasons) and differences in a mean value. Although only one p-value in a mean test allows to reject the null in 5% level, other p-values are relatively small and can suggest important differences in mean. One can support that findings by results of Table 2 and visualizations of Fig 3, 4 and 5. All together leads to conclusion that 2020 season was more heterogeneous than the rest of the sample in terms of teams and track preparation. Some teams did win by great number of points when others did lose highly, as well. Home track was not so important handicap as usually, which could mean that there were lack of time for training in home objects and lack of careful preparation of home track as well. That findings are in accordance with 2020 season delay and national lockdown in Poland. Moving to part two of the research, analysis of points and age of teams showed significant structural difference of season 2020. Shape of empirical distribution of points collected by teams confirmed increased variation in scores and a lack of concentration around the average number of points. There was a weak negative, statistically significant correlation between points collected by team and team’s average age in all of the seasons, expect season 2020 and 2016. In a season 2020 the lack of correlation is evident in terms of both rho and p- value, when result for 2016 is more vague. Cluster analysis confirmed that in a season 2020 there were two clusters according to the average age of the teams. One can describe cluster 1 as “older” teams’ cluster, with average age of a team equal to 28.83 years. Cluster 2 can be named as “younger” teams’ cluster with average age of 25.11 years. Median number of points collected by the teams in clusters were: 45.5 for “younger” and 44 for “older”, however from the Kruskall – Wallis test one can learn that the difference in medians is not statistically significant. It implies that both groups of teams performed equally well. From managerial point of view it could mean that there were two equally good team building strategies in terms of age structure in season 2020. In a contrary to season 2020, in a second sample there were 5 clusters of teams (on average) with significantly different effectiveness measure as median of points collected. The most important conclusions from the third part of the research were as follow. Only in season 2020 probability of fall of a young rider was significantly greater than probability of fall of an older rider. It could ------981 JPES ® www.efsupit.ro SYLWESTER BEJGER ------mean that lack of track trainings and sparing meetings in a pandemic season of 2020 was particularly severe for the preparation for riding in a group of younger riders. In a season 2020 older riders started in 516 heats (the highest number in a whole sample) and collected second highest sum of points in the all seasons. Younger riders performs much worse, with the smallest sum of points collected and second smallest mean of points. Taken together results of part two and three, it implies two different but equally effective team building strategies - younger teams, which consisted of only a few older riders who scored above average, and older teams consisting of several older riders, who scored on average. Taking into consideration internationalisation of teams, examination showed that international riders were similarly intensively exploited in season 2020 as in season 2019 but their performance were better and their shape was more stable. Polish riders showed highly unstable shape (high variance of points collected). These two facts lead to the conclusion that from the managerial point of view, in a lock-down conditions managers and coaches need to pay more attention to the preparation of the Polish riders and should exploit stable shape of international riders.

Conclusions The significant impact of the extraordinary external conditions of the 2020 season on various sports seems obvious, but its exact determination requires scientific research. This article covers such preliminary research on speedway. A statistical analysis of the meetings in Polish PGE Ekstraliga in the 2020 season and in the years 2015- 2019 revealed the facts about the difference between the first season of the pandemic and the previous ones. An examination showed that average performance of the best group of riders in the league, measured by best time of heat in a meeting, was not significantly different in season 2020 and previous 5 seasons in terms of mean time of a heat. It means that the leading group of riders was performing similar to non-covid seasons. However empirical distribution of best times in 2020 was significantly different form previous years in 3 cases of 5, which suggests that there was structural changes in performance distribution. Values of both skewness and kurtosis of empirical distribution suggest more flat distribution than in previous years (apart 2016 season), which can mean that preparation of tracks in 2020 season was more unequal. Teams’ average sport level measured by difference in scores occurred to be more diverse in pandemic season as well. It leads to conclusion that 2020 season was more heterogeneous than the rest of the sample in terms of teams and track preparation. That findings are in accordance with 2020 season delay and national lockdown in Poland which caused lack of time and conditions for trainings and careful track maintenance. Another significant consequence of the disruptions of the 2020 season was the greater number of falls of younger riders. The probability of fall of a young rider was significantly greater than probability of fall of an older rider in pandemic season only. It could mean that lack of active preparation was particularly severe for the younger riders. Taking into consideration nationality of riders in the teams, examination showed that foreign riders were similarly intensively exploited in season 2020 as in season 2019 but their performance were better and their shape was more stable. The shape of Polish riders was more diverse. To summarize, the study revealed that the first pandemic season were in fact different than the other seasons in Polish PGE Ekstraliga taking into considerations various measures describing performance of the teams and the riders. Observed oddities drive to managerial implications formulated in a discussion section. The results of this and similar studies seem to be important because they allow us to answer the question of how clubs, teams and players adapted to the changed conditions of functioning during pandemic. These findings can help club managers and coaches formulate more effective policies for such circumstances in a future.

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